Outlier-robust tri-percentile and truncated maximum likelihood estimators of parameters of weibull radar clutter

Abstract

Weibull distributions have gained much concern for the versatility in modelling radar clutter such as sea, ground, and weather clutters. Most existing parameter estimation methods are sensitive to outliers and have degraded accuracy in real clutter environments with outliers. This paper proposes two classes of outlier-robust parameter estimators of Weibull distribution. One is the tri-percentile (TriP) estimator, where the shape parameter is estimated from the ratio of two sample percentiles and the scale parameter is estimated from the third sample percentile. The relative root mean square error (RRMSE) of the shape parameter is proved to be independent of the two parameters. Moreover, the optimal position setup of the percentiles is chosen to minimize estimation errors. The other is the iterative truncated maximum likelihood (TML) estimator, which obtains more accurate robust estimates. It is shown that the RRMSE of the shape parameter is also independent of the two parameters. The ML estimator is a special example of the iterative TML estimator. Finally, experiments with simulated data and measured radar data are made to compare the performance of the TriP and TML estimators with that of the ML estimators and other existing estimators in the presence of outliers in data.